There has been a strong interest in the systems of the form (REF ) in scientific literature starting somewhere in the middle 20th century.
The most popular object of study from the class of systems (REF ) is the Lorenz system [1]}:
\(\left\lbrace \begin{array}{l}\dot{x}_1=\sigma (x_2-x_1),\medskip \\\dot{x}_2=rx_1-x_2-x_1x_3,\medskip \\\dot{x}_3=x_1x_2-bx_3.\end{array}\right.\endequation For this system, the matrices have the form:\begin{array}{c}B_0=\textbf {0},\:\:\:B_1=\left[\begin{array}{ccc}-\sigma & \sigma & 0\medskip \\r & -1 & 0\medskip \\0 & 0 & -b\end{array}\right],\:\:\:Q_1=\textbf {0},\medskip \\Q_2=\left[\begin{array}{rrr}0 & 0 & -1\medskip \\0 & 0 & 0\medskip \\0 & 0 & 0\end{array}\right],\:\:\:Q_3=\left[\begin{array}{rrr}0 & 1 & 0\medskip \\0 & 0 & 0\medskip \\0 & 0 & 0\end{array}\right].\end{array}\) 
